Optical lithography has been the dominant technology for the patterning of semiconductor device features. As the size of the geometry for these devices continue to shrink below the ultraviolet (UV) wavelength used for imaging, significant demands are placed on the quality of the optical component within the projection imaging system. Projection systems used for microlithographic imaging or micro-optical inspection comprise a large number of lens elements and operate at wavelengths ranging from 436 nm to 126 nm. The level of aberration in these systems must be low enough to allow imaging on the order of 0.30 lambda/NA, where lambda is the imaging wavelength and NA is the numerical aperture of the lens system, typically on the order of 0.40 to 1.2. This type of performance is near the physical limits of diffraction and aberrations must be low enough to produce optical wavefront deformation in the projection lens pupil below a multiple of 0.1 wavelengths, and approaching 0.001 wavelengths for the most advanced systems.
Lens quality can be described in terms of the ability of an optical system to convert the spherical wavefront emerging from an object point into a spherical wavefront converging toward an image point. Each aberration type will produce unique deviations in the wavefront within the lens pupil.
For a system utilizing full circular pupils, Zernike circle polynomials can be used to represent optimally balanced classical aberrations. Any term in the expansion of the wave aberration function leading to a complete set of Zernike polynomials can be represented as:
      W    ⁡          (              ρ        ,        θ            )        =            ∑              n        =        0            ∞        ⁢                  ∑                  m          =          0                n            ⁢                                    2            ⁢                                          (                                  n                  +                  1                                )                            /                              (                                  1                  +                                      δ                                          m                      ⁢                                                                                          ⁢                      0                                                                      )                                                    ⁢                                            R              n              m                        ⁡                          (              ρ              )                                ⁡                      [                                                            c                                      n                    ⁢                                                                                  ⁢                    m                                                  ⁢                                  cos                  ⁡                                      (                                          m                      ⁢                                                                                          ⁢                      θ                                        )                                                              +                                                s                                      n                    ⁢                                                                                  ⁢                    m                                                  ⁢                                  sin                  ⁡                                      (                                          m                      ⁢                                                                                          ⁢                      θ                                        )                                                                        ]                              where n and m are positive integers (n−m≧0 and even), cnm and snm are aberration coefficients, and the radial polynomial R of degree n in terms of the normalized radial coordinate in the pupil plane (ρ) is in Mahajan's convention [V. N. Mahajan, Zernike circular polynomials and optical aberrations of systems with circular pupils, Eng. and Lab Notes, in Opt. & Phot. News 5, 8 (1994)]. Commonly, a set of 37 Zernike polynomial coefficients is utilized to describe primary and higher order aberration, although some applications may require additional terms.
Since any amount of aberration results in image degradation, tolerance levels must be established for lens system, dependent on application. This results in the need to consider not only specific object requirements and illumination but also process requirements. Conventionally, an acceptably diffraction limited lens is one which produces no more than one quarter wavelength (λ/4) wavefront OPD. For many lens systems, the reduced performance resulting from this level of aberration may be allowable. This Rayleigh λ/4 rule is not suitable however for high resolution applications such as microlithographic imaging or micro-optical inspection applications. To establish allowable levels of aberration tolerances for a these applications, application specific analysis must be performed. Detector requirements need to be considered along with process specifications. As an example, the current needs of UV and DUV lithography require a balanced aberration level below 0.03λ OPD RMS. Future requirements will dictate sub-0.01λ performance. More important, however, may not be the full pupil performance but instead the performance over the utilized portion of the pupil for specific imaging situations [B. W. Smith, Variations to the influence of lens aberration invoked with PSM and OAI. Proc. SPIE 3679 (1999)].
Aberration metrology is critical to the production of micro-optical quality projection lenses in order to meet these strict requirements. Additionally, it is becoming increasingly important to be able to measure and monitor lens performance in an application environment. The user needs to understand the influences of aberration on imaging and any changes that may occur in the aberration performance of the lens between lens assembly and application or over the course of using an exposure tool.
The most accurate method of measuring wavefront aberration (and subsequently fitting coefficients of Zernike polynomials) is phase measurement interferometry (PMI), also known as phase shifting interferometry (PSI) [J. E. Greivenkamp and J. H. Bruning, Optical Shop Testing: Phase Shifting Interferometry, D. Malacara ed, (1992) 501]. PMI generally describes both data collection and the analysis methods that have been highly developed for lens fabrication and assembly and used by all major lithographic lens suppliers. The concept behind PMI is that a time-varying phase shift is introduced between a reference wavefront and a test wavefront in an interferometer. At each measurement point, a time-varying signal is produced in an interferogram. The relative phase difference between the two wavefronts at this position is encoded within these signals.
The accuracy of PMI methods lies in the ability to sample a wavefront. A wavefront can be sampled with a spacing of λ/n where n is the number of times the system is traversed by a test beam. These methods require careful control of turbulence and vibration. A more significant limitation of these interferometric methods in the need for the reference and test beams to follow separated paths, making field use (or in-situ application) difficult. One is therefore restricted to using alternative approaches to measure, predict, approximate, or monitor lens performance and aberration during application of the optical system.